Dendritic integration in a recurrent network

Classical nonlinear cable theory is appropriate for the unmyelinated axonal membrane because voltage-dependent ion channels are densly distributed, but dendrites with a sparse density distribution of voltage-dependent ion channels show "weakly" excitable membrane properties. Therefore, a model for "weakly" active dendrites is presented by introducing voltage-dependent ion channels at discrete locations along the dendritic cable. This provides an alternative representation for the investigation of regenerative potentials in dendrites in order to explore how active dendrites influence synaptic integration. As an example, we consider a two-neuron recurrent network of biophysically distinct conductance-based model neurons with discrete clusters of persistent sodium channels. Analytical solutions, expressed in terms of a Volterra series expansion for the voltage in response to a suprathreshold input current at the soma of one neuron, are obtained to investigate dendritic spikes, and the effect of backpropagation on distal dendritic spike-like potentials.